Statistica Sinica 15(2005), 3-18
IMPROVING ON THE INDEPENDENT
METROPOLIS-HASTINGS ALGORITHM
Yves F. Atchadé and François Perron
Harvard University and University of Montreal
Abstract:
This paper proposes methods to improve Monte Carlo estimates when the
Independent Metropolis-Hastings Algorithm (IMHA) is used.
Our first approach uses a control variate based on the sample generated by the
proposal distribution. We derive the variance of our estimator for a fixed
sample size 
and show that, as tends to infinity, this variance is
asymptotically smaller than the one obtained with the IMHA.
Our second approach is based on Jensen's inequality. We use a
Rao-Blackwellization and exploit the lack of symmetry in the IMHA.
An upper bound on the improvements that we can obtain by these methods is
derived.
Key words and phrases:
Control variates, Metropolis-hastings algorithm,
Rao-Blackwellization, symmetry.